The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by

- A
$\{(1, 4, (2, 5), (3, 6),.....\}$

- B
$\{(4, 1), (5, 2), (6, 3),.....\}$

- C
$\{(1, 3), (2, 6), (3, 9),..\}$

- D
None of these

Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, b) \in R,$ implies $(b, a) \in R$

Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$

Depict this relation using an arrow diagram.

Let $A=\{1,2,3,4\}, B=\{1,5,9,11,15,16\}$ and $f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$

Are the following true?

$f$ is a relation from $A$ to $B$

Justify your answer in each case.

The Fig shows a relation between the sets $P$ and $Q$. Write this relation

in roster form

What is its domain and range ?

Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$